The customer pays part now and the rest later, or in instalments. What do I do?

Nothing special. The invoice is written once, for the full amount, and sent to ZATCA. Payments are recorded as receipts against that invoice, and none of them goes to ZATCA; ZATCA doesn't care when the customer pays.

Example: a 100,000 invoice is sent to ZATCA. The customer pays 30,000 now (a receipt), 20,000 six months later (a receipt), and the rest a year later. One invoice was sent, and the system always knows what is left.

Instalments in the system are only a collection schedule; the invoice itself is sent once.